archived as http://www.stealthskater.com/Documents/Time_04.doc [pdf]
more related articles at http://www.stealthskater.com/Science.htm#superstrings
note: because important websites are frequently "here today but gone tomorrow", the following was
archived from http://physics1.usc.edu/~bars/research.html#2T on October 12, 2007. This is NOT
an attempt to divert readers from the aforementioned website. Indeed, the reader should only read
this back-up copy if the updated original cannot be found at the original author's site.
Itzhak Bars' Research Interests
[note: a layman's essay on Dr. Bars' 2T-Physics appeared at
http://www.telegraph.co.uk/earth/main.jhtml?xml=/earth/2007/10/10/scitime110.xml
and is also archived at doc pdf URL-doc URL-pdf .]
My current interests include mainly String Field Theory (SFT) and Two-Time Physics (2TPhysics). But these are related to several other topics in which I am currently active as outlined below.
Some of my early contributions to string theory include the non-trivial quantization of the twodimensional string and the first treatment of 1-branes interacting with 0-branes (interpreted as quarks at
the ends of a string). This work established a firm and explicit relation between string theory and
large-N QCD in 2 dimensions.
The more recent AdS-CFT correspondence includes an analogous endeavor that establishes a
relation between field theory and string theory in one higher dimension. The AdS-CFT approach mainly
involves the gauge sector as opposed to the matter sector treated in my early work. How to make use of
such ideas to make progress in real QCD in 4 dimensions is one of the challenges that I think about.
The action for the superparticle suggested in 1981 by Brink & Schwarz was discovered earlier in
1975 in the context of supersymmetric quarks at the ends of a string. The covariant quantization of
the superparticle and superstring continue to be a challenge today and is part of my research on the way
to the supersymmetric generalization of string field theory.
In the conformal field theory era of string theory, I emphasized the importance of strings moving in
backgrounds with curved space-time since string theory should play its main role during the (surely
curved) early Universe. With this in mind, I introduced some of the first exactly solvable string
models in curved spacetime including the SL(2,R)/R model which was later understood by Witten to be
a model for strings on black holes. I continue to research this general topic in the context of string field
theory and cosmology.
My interest in higher dimensions began by providing the first evidence that 11 dimensions is critical
for the quantum consistency of the supermembrane. After the strings-95 conference that marked the
second superstring revolution, I emphasized in my 1995 talks that structures based in (10,2) dimensions
were evident in the extended algebra of M-theory.
Soon afterwards, papers suggesting more time-like dimensions began to appear. This led to my
proposal of an algebraic S-theory in 1996 which helped develop some 2T notions in collaboration with
Costas Kounnas. Finally that approach developed into a rather basic and fundamental dynamical form
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based on Sp(2,R) gauge symmetry in a 1998 paper with Oleg Andreev and Cemsinan Deliduman and
then transformed into a general 2T-physics theory in its own right.
Later, I found connections to some work by Dirac in 1926 and Salam in the 1970s in connection
with conformal symmetry SO(d,2) (one extra space and one extra time compared to Lorentz symmetry
SO(d-1,1) ), which can now be understood as some of the consequences of 2T-physics. The sort of
symplectic gauge symmetry of 2T-physics may well explain the duality and holographic properties of
the mysterious M-theory.
My work on 2T field theory based on the Moyal product is what led me to discover the Moyal star
formulation of string field theory (MSFT). This was motivated by the observations that on the one hand,
a very similar formalism of non-commutative field theory and Chern-Simons type actions emerged
naturally in both cases. And on the other hand, bosonized ghosts in string field theory play a role similar
to a second time-like coordinate.
Through MSFT, I set out to learn something from string field theory to apply it to 2T-physics. I
hope to bring the experience of MSFT back into 2T-physics and get to a higher level of unification.
String Field Theory (SFT)
Since the early stages of string theory in the 1970s, string field theory (SFT) was recognized to be a
non-perturbative approach to string theory. Among all the formulations of string theory since its
inception, string field theory stands out as the most complete scheme as a non-perturbative formulation
that seems -- in principle -- to be better positioned to answer the central physics questions.
One of the main goals of SFT (and indeed of all the efforts in string theory) is understanding the
vacuum state and how we ended up in 4 dimensions. This includes elucidating the physics of the very
early Universe and how this determined the gauge symmetries (forces) and the families of quarks and
leptons (matter) that we observe today.
Many attempts have been made over the past 30 years to formulate and develop computational tools
in SFT. While all of these approaches were correct, the proposed formalisms were too cumbersome to
extract easily non-perturbative or even perturbative information about string theory.
In 2001, I introduced the Moyal Star Formulation of String Field Theory (MSFT) as a computational
framework for Witten's cubic open string field theory. The novelty was that string interaction was reformulated in terms of the simple Moyal product indicative of an induced quantum mechanics which is
produced by string joining.
The advantage of MSFT is that the resulting non-commutative field theory is much simpler for
practical computations because the Moyal star product replaces conformal field theory or the oscillator
approach in all SFT computations. This leads to new non-perturbative computational techniques
directly in MSFT without recourse to cumbersome maps to conformal field theory which is anchored
essentially in perturbative string theory.
MSFT is now the simplest description of string interactions in the context of a complete and
nonperturbative formulation of open string theory. Having demonstrated that D-branes -- as well as
closed strings -- emerge non-perturbatively in open string field theory, it is quite possible that a
supersymmetric version of MSFT (still to be achieved) will amount to some version of the complete Mtheory.
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Much of the new computational technology was developed with my collaborators Yutaka Matsuo
and Isao Kishimoto. And more recently with Inyong Park. We have applied MSFT to both perturbative
string physics (new results for off-shell string amplitudes) and non-perturbative string physics (analysis
of the true vacuum of string theory, D-branes).
In these areas, MSFT has yielded new results that were not obtained before while at the same time
we have verified that MSFT is in detailed agreement with other approaches to string theory (conformal
field theory, oscillator formalism etc.).
Finding the true vacuum is one of the most important challenges in string theory. We introduced an
analytic approach and applied it to the solution of the classical string field equations including
interactions. It was possible to obtain all exact solutions -- including the vacuum solution -- when an
anomalous term in the energy of the midpoint of the string is neglected. The anomalous midpoint
energy was then treated as a perturbation and the first two terms were computed. This ongoing program
is expected to yield analytic insight into the true vacuum of string theory.
Ongoing projects include generalizing the MSFT approach to strings in curved backgrounds (I have
in mind applications to early cosmology) and supersymmetrization in the covariant Green-Schwarz or
Berkovits formalism (which will amount to a full definition of a version of M-theory). I have already
achieved the first important step of formulating the generalization of the Moyal star product for strings
in these conditions and will next construct the BRST operator, which will complete the definition of the
theory. After that, I will be looking forward to many applications.
Two-Time Physics (2T-physics)
Starting with the 1998 formulation of Two-Time Physics (2T-physics) -- which was inspired by 2T
notions in earlier papers since 1995 -- evidence has been mounting that the ordinary formulation of
physics in a space-time with three space and one time dimensions (1T-physics) is insufficient to describe
our world.
A one-page summary of the concepts of 2T-physics can be found in this diagram (not up to date)
with related narrative below. (For technical information, please refer to my original papers.)
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According to the body of work in 2T-physics, there is more to space-time than can be garnered with
1T-physics. 2T-physics introduces additional one space and one time dimensions which can coexist
with the familiar 3+1 dimensions as well as extra space dimensions of tiny sizes known as KaluzaKlein-type dimensions. But the new ones have very different properties.
First of all, the extra 1+1 dimensions in 2T-physics are not small. However, there are gauge
symmetries that effectively reduce 2T-physics in 4+2 dimensions to 1T-physics in 3+1 dimensions
without any Kaluza-Klein remnants. The reduction is not unique because there is an infinite variety of
3+1 embeddings in 4+2 dimensions (more generally (d-1)+1 in d+2). And this is what is non-trivial and
rich in emergent space-times and 1T-physics content.
To help grasp the relation between 1T-physics and 2T-physics, consider the many possible shadows
of a 3-dimensional object projected from different perspectives on the surrounding walls of a 3dimensional room. A "flatlander" that can crawl and measure only on the surface of the walls would
think that the shadows of different shapes are different “beasts” and move differently. Similarly, even
though according to 2T-physics a unique dynamical system in 4+2 dimensions generates a large variety
of 1-time “shadows”', 1T-physics presents these “shadows” in 3+1 dimensional space-times as different
dynamical systems in terms of different Hamiltonians (different times).
In this way, 1T-physics misses the underlying relationship between the “shadows” as well as the
underlying properties (e.g. symmetries) of the higher dimensional space-time. Actually, it turns out that
each “shadow” is a holographic image that retains all the information of the d+2 structure. This
information takes the form of hidden symmetries, dualities, and other non-trivial structures which are
hard to notice by the 1T physicist that investigates the “shadows” (i.e. different dynamical systems).
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But he/she could in principle discover the hidden information. 2T-physics provides the missing
information to the 1T physicist who can verify by experiment or computation that indeed the d+2
structure of space-time governs all levels of physics -- from Macroscopic to microscopic scales, in
classical and quantum systems, including the fundamental physics of quarks, leptons, and force particles
described by the Standard Model of Particles and Forces, and beyond.
The permitted motions in 4+2 phase space are highly symmetrical as they are constrained by a
Sp(2,R) gauge symmetry that makes momentum and position indistinguishable at any instant. Such
Sp(2,R) symmetric motions in 4+2 dimensions are completely compatible with the way physics is
perceived in 3+1 dimensions. In particular, there are no problems with causality or unitarity because the
extra 1+1 space-time (chosen in distinguishable ways from the point of view of 1T-physics) is
removable by the gauge symmetry.
The two time-like dimensions were not introduced whimsically “by hand”. As mentioned above,
2T-physics is based on gauging the symplectic transformations Sp(2,R) acting on phase space (XM,PM).
One of the fundamental results of this new gauge principle is that in order to be nontrivial, it requires the
theory to be formulated in a space-time having at least two times. While taking exactly two time-like
dimensions produces a coherent theory, investigations of alternatives with more than two times have
been done (including alternatives to Sp(2,R)). So far such possibilities are ruled out because of
problems with ghosts and unitarity. And this seems to confirm the special status of 2T-physics.
Recently, a field theoretic description of 2T-physics has been established. Amazingly, the best
understood fundamental theory in Physics -- the Standard Model of Particles and Forces (SM) in 3+1
dimensions -- is reproduced as one of the “shadows” of a parent field theory in 4+2 dimensions.
But even more amazing is that this emergent SM has better features than the ordinary SM in 1Tphysics. Among the successes of the emergent SM is the resolution of the strong CP problem of QCD
due to the more constraining structure of the underlying 4+2 theory. This suggests that the so far elusive
axion need not exist at all since the issues in the fundamental theory are resolved with the gauge
mechanisms of 2T-physics. The emergent SM agrees with all aspects that actually work experimentally
so far in the usual SM.
The field theoretic studies of 2T-physics have been generalized to supersymmetric field theory
with N=1,2,4 supersymmetry. It is expected that the more constraining structure of the underlying 4+2
theory has phenomenological consequences that would be relevant to distinguish 2T-physics from other
approaches in experiments at the LHC starting in 2008 if supersymmetry is found experimentally at the
TeV scale.
The field theory version of 2T-physics suggests new emergent principles in field theory. These have
been enunciated in a paper that explores dual field theories in (d-1)+1 emergent spacetimes from a
unifying field theory in d+2 space-time.
Prior to recent success in field theory, the work on 2T-physics since 1998 had mostly concentrated
on the worldline formalism of particles. And it had demonstrated that 2T-physics stands above 1Tphysics as a structure that encompasses and explains phenomena which appear very surprising from the
point of view of 1T-physics.
The prior work on 2T-physics during 1998-2004 extended the initial concepts in several directions,
including spinning particles, supersymmetry, and interactions of particles with background fields
(electromagnetism, gravity, and all higher spin fields). Covariant quantization of 2T systems led to field
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theoretic equations of motion but without an action principle, and a non-commutative approach was
developed for 2T-field theory in phase space.
There was also some limited work on the world-sheet or world volume level for the 2T-physics
formulation of strings and branes. Some hidden 10+2 or 11+2 structures in supergravity and M-theory
-- in the AdS5 x S5 and other compactifications -- were also identified and explained as features of 2Tphysics.
After some excursions into String Field Theory during 2001-2004 to explore non-commutative
aspects, extensive research on 2T-physics resumed in 2004-2005. This was sparked by the twistor
superstring and its relation to the twistor gauge of 2T-physics. New unifying roles for twistors were
discovered and a new approach to spinning particles led to a new hidden SU(2,3) duality symmetry that
includes conformal symmetry SU(2,2).
These older results (along with the more recent field theory successes mentioned above) have
established that 2T-physics is a structure that correctly describes -- at least in principle -- all the physics
we have understood up to now. But 2T-physics emerged also as a unification scheme that suggests the
existence of new relationships and new phenomena that are not even hinted by 1T-physics and which
remain so far largely unexplored both theoretically and experimentally.
This 2T-physics point-of-view provides new mathematical tools and new insights for understanding
our Universe. It also suggests a new paradigm for the construction of a fundamental theory that is likely
to impact on the quest for unification.
For systems that are already understood, 2T-physics tells us that the description of dynamics via the
usual 1T-formalism should be interpreted as emergent dynamics that holographically represents an
image of a deeper higher dimensional structure in one extra space and one extra time. A lot more work
awaits to be done in this direction to reveal the hidden dimensions in various 1T systems including in the
field theory formalism.
[StealthSkater note: There was a book entitled The Holographic Universe. Whether this
was a forerunner to any of Prof. Bars' theses, I am not sure. Nor am I sure of any of the
following which came to my mind as I read the above.
Former electrical engineering professor Ray Kramer (father of famed missing person
Philip Taylor Kramer) had proposed his own "Theory of Everything" in something he called
"the Equation". Reportedly his son (an expert in fractal geometry) accidentally solved it when
he "plugged" it into another problem that he was working on. It claimed to permit
instantaneous communication anywhere within the Universe as well as -- more mysteriously -possible biological teleportation => doc pdf URL .
Famed German rocket pioneer Hermann Oberth allegedly said that UFOs (or perhaps
more precisely, the one he allegedly examined [Roswell?] ) appeared to function more as "time
machines" of some sort than advanced flying craft doc pdf URL . And proponents of the
"Montauk Project" have claimed that it inadvertently accessed "timelines" already existing =>
doc pdf URL . Some theories of the "Philadelphia Experiment" said that it was based on a
discovery made by Nikola Tesla where he saw that by applying certain magnetic and electrical
fields, an object could be made to reverse along its previously-established path on his
workbench. Supposedly this found its way into WWII minesweepers which could regress
along a history path when it was too late to avoid a mine => doc pdf URL .
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And there are the "intuitive communication" claims of former ELINT Sgt. Dan Sherman
with off-world Aliens in which they allegedly said that they did not travel "through" time (that
was impossible) but "evaded" time ( doc pdf URL ). Perhaps this "evasion" was what Prof.
Bars was referring to as the other time dimension?
Finally, this additional time dimension makes me remember what Tom Bearden has been
saying all along involving "unobservables" in a "scalar time domain" => doc pdf URL ]
Ultimately we expect 2T-physics to be useful not only for insights into the deeper structures, but also
as a calculational tool that takes advantage of the dualities and hidden symmetries in 1T-physics
field theory.
For systems that are not yet understood or even constructed (such as M-theory), 2T-physics points to
a possible approach for a more symmetric and more revealing formulation in 11+2 dimensions that can
lead to deeper insights, including a better understanding of space and time. The 2T approach could be
one of the possible avenues to construct the most symmetric version of the fundamental theory.
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